Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class carrotcutting {

    static int n;
    static double h,a, h1[],x1[];
    static double INF = 1e-12;

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        n = Integer.parseInt(st.nextToken());
        h = Double.parseDouble(st.nextToken());
        h1=new double[n-1]; x1=new double[n-1];
        a = 0.5*h/n;
        h1[0] = h/Math.sqrt(n);x1[0]=1/Math.sqrt(n);
        for (int i = 1; i < n-1; i++) {
            h1[i]=h1[i-1]+find(i, x1[i-1]);
        }
        for (int i = 0; i <n-2 ; i++) {
            System.out.print(h1[i]+" ");
        }
        System.out.println(h1[n-2]);


    }
    public static double find(int i,double top){
        double lo=a, hi=h-h1[i-1];
        double mid=(lo+hi)/2;
        while (hi-lo>INF) {
            double bottom = (mid+h1[i-1])/h;
            x1[i]=bottom;
            double a1=0.5*(bottom+top)*(mid);
            if ((Math.abs(a1-a)<INF)){
                return mid;
            }
            if ((a1-a)>INF){
                hi=mid;
            } else{ //if (a1-a<INF)
                lo=mid;
            }
            mid=(lo+hi)/2;
        }
        return hi;
    }

}